## MA50170: Numerical solution of elliptic PDEs

[Page last updated: 05 August 2021]

Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Masters UG & PG (FHEQ level 7)
Period:
Semester 2
Assessment Summary: CW 25%, EX 75%
Assessment Detail:
• Coursework (CW 25%)
• Examination (EX 75%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: In taking this module you cannot take MA30170 . Before taking this unit you must take MA20222 or an equivalent first course in numerical analysis.
Description: Aims:
To teach the finite element method for elliptic PDEs based on variational principles.

Learning Outcomes:
At the end of the course, students should be able to derive and implement the finite element method for a range of elliptic PDEs in one and several space dimensions, including problems with random coefficients. They should also be able to derive and use elementary error estimates for these methods. They should be able to demonstrate an in-depth understanding of the subject.

Skills:
Understanding of the finite element method (T, A), Computer programming with the finite element method (T, A).

Content:
Introduction. Variational and weak form of elliptic PDEs. Natural, essential and mixed boundary conditions. Linear and quadratic finite element approximation in one and several space dimensions. An introduction to convergence theory. System assembly and solution, isoparametric mapping, quadrature, adaptivity. Applications to PDEs arising in applications. PDEs with random coefficients. Examples of intrusive and non-intrusive methods (e.g., Monte Carlo methods and stochastic Galerkin methods).

Programme availability:

#### MA50170 is Optional on the following programmes:

Department of Mathematical Sciences

 Notes: This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22. Programmes and units are subject to change in accordance with normal University procedures. Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules. Find out more about these and other important University terms and conditions here.